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Brazilian Journal of Physics, vol. 34, no. 1, March, 2004 3

A Review on the Dynamics of Water

Milton T. Sonoda, Ney H. Moreira, Leandro Martınez, Frank W. Favero,Sergio M. Vechi, Lucimara R. Martins, and Munir S. Skaf

Instituto de Quımica, Universidade Estadual de Campinas, Cx. P. 6154, Campinas, SP, 13084-971, Brazil

Received on 17 October, 2003.

We present a review on the intermolecular dynamics of liquid aqueous systems focusing mainly on Molecu-lar Dynamics simulation work that has been carried out at the State University of Campinas in recent years.Emphasis is given on simulation results that are more directly related to modern experimental spectroscopicmeasurements.

1 Introduction

Water is by far the most important, most ubiquitous, moststudied, and yet one of the least understood liquids on Earth.The strength and high directionality (anisotropy) of the in-termolecular interactions in water lead to highly peculiarthermodynamic and structural properties [1-4]. The na-ture of the intermolecular interactions allied to water’s lowmolecular weight and small moments of inertia, allow for acomplex pattern of intermolecular force fluctuations in bothlength and time scales, promoting a dynamical behavior thatis unique to water[3, 4]. At the heart of water’s intrigu-ing behavior lies the network of hydrogen (H) bonding. Inaddition, manifestations of inherently quantum mechanicaleffects on water’s macroscopic behavior brings in an addi-tional degree of challenge, and fascination, to this field ofresearch[5].

The intermolecular dynamics of liquid water has longbeen subject of intense experimental and theoretical re-search. Numerous experimental studies have been re-ported on the dynamics of this liquid using a varietyof different techniques, including microwave dielectricrelaxation[6], far-infrared[7], Raman[8] and light scatter-ing spectroscopies[9], NMR[10], and small angle neutronscaterring[11] in the last two or three decades. Morerecently, new experimental developments based on ultra-fast laser techniques have made it possible to investi-gate intermolecular dynamical processes of water at muchshorter timescales with substantially higher level of detail.Among these, terahertz spectroscopy[12] and nonlinear op-tical methods such as Raman echo[13] and optical Kerr ef-fect (OKE)[14] spectroscopies stand out for providing re-markably valuable information directly in the time domain.

Parallel to these developments, advances in moleculardynamics (MD) computer simulations have markedly en-riched our views on the dynamics of water, both at ambientand extreme conditions of temperature and pressure[3, 4].A variety of MD simulation studies have been performedon liquid water aiming to understand different aspects of itsdynamics by means of interaction potentials of distinct com-

plexity. In particular, detailed simulation analyses have beenreported for the dielectric relaxation, depolarized Raman orlight scattering, time resolved fluorescence spectroscopy[3],and nonlinear optical Kerr response for bulk phases[15], aswell as second harmonic generation and vibrational sumfrequency[16] signals for studying interfacial systems morespecifically. In this work, we present a nonpretentious re-view on the dynamics of liquid water and other aqueous sys-tems that focuses especially on our own recent work with anemphasis on simulations of physical observables of spectro-scopic relevance. Some of the results presented here havenot heretofore been published. We shall not discuss any as-pects related to techniques of MD simulation and will notreview the numerous Hamiltonian models available for wa-ter nor the description they provide for the physicochemicalproperties of the fluid. The purpose here is to provide anoverall physical picture for the underlying water dynamicswithin different contexts, as obtained from MD simulations.

The paper evolves from a tutorial review on the funda-mental characteristics of the dynamics of liquid water de-scribed in terms of single-particle motions to an abrigedpresentation of MD studies of distinct spectroscopic prop-erties of selected aqueous systems including: i) Dielec-tric relaxation and far-infrared spectroscopies of water,water-methanol and water-dimethylsulfoxide (DMSO) bi-nary mixtures, and supercritical water; ii) Ultrafast time-resolved spectroscopy of coumarin dyes in water and water-DMSO mixtures, and of excess hydrated electrons; iii) Non-linear optical spectroscopy of water; iv) Vibrational dephas-ing of the squarate anion in water; and v) Water near inter-faces. The paper concludes with a brief description of therole of water in the dissociation of the retinoic acid from itsnuclear hormone receptor.

2 Single-particle dynamics

The seminal MD simulations of Rahamn and Stillinger somethirty years ago provided the first look into the molecularmotions of liquid water[17]. Detailed knowledge on the

4 Milton T. Sonodaet al.

translational motions of individual atoms or the moleculeas a whole, as well as the molecular rotational motions ismost commonly described in terms of the time correlationfunctions (TCF),CO(t) = 〈O(t) · O(0)〉 / ⟨|O(0)|2⟩, withthe dynamical variableO(t) being the linear velocities ofindividual atoms (vO, vH ) or the molecular angular velocitycomponents (Γx,y,z). Linear and angular velocity TCFs ob-tained from MD simulations using the SPC/E model[18] aredepicted in Fig.1 (upper panels) along with their frequencyspectra obtained from the cosine Fourier transforms (lowerpanels). The dynamics we see here refer to intermolecu-lar motions only. Intramolecular vibrational motions are notportraied in Fig.1 because the SPC/E model lacks internaldegrees of freedom. Notice how the TCFs rapidly convergeto vanishing amplitudes within 100 – 500 fs. This gives anidea of how fast are the collision rates in liquid water. Theshort-time dynamics of the O and H atoms are suggestive ofdamped oscillatory motions and result from the interactions(“collisions”) with neighboring molecules. These featuresresemble somewhat the dynamics of solids. The transla-tional velocity TCF of the O atoms exhibits a negative por-tion due to the back scattering motions of the molecule in-side the H-bonded cage of neighbors. The dynamics of theH atoms in this time scale is much faster because of theirsmall masses. Translational motions of H atoms is highlycorrelated to rotations of the molecule as a whole around thecenter of mass and this is why theCvH(t) andCΓ(t) func-tions are similar. TheCΓ(t) TCFs indicate very clearly theexistence of small amplitude, hindered or damped rotationaloscillations known as librations. The librational period liesbetween 20 and 40 fs. These fast rotational oscillations ap-pear so prominently in water because of the small momentsof inertia and the existence of high molecular torques due toH-bonding restoring forces[3, 17]. The differences observedbetween the angular velocity components correlate with themagnitude of the moments of inertia,Ixx = 1.0 × 10−47

kg/m2 (parallel to the HH vector),Iyy = 1.9×10−47 kg/m2

(main symmetry axis), andIzz = 2.9 × 10−47 kg/m2 (nor-mal to plane): Smaller moment means faster rotation aboutthe corresponding principal axis.

The characteristic frequencies associated with these mo-tions are reflected in the Fourier spectra. The hindered trans-lational motions of the molecule (O atom) inside the cageof neighbors have a main frequency component around 250cm−1. A small shoulder can be seen around 60 cm−1. Thespectral characteristics of the librations consist of a broadband between 400 and 1000 cm−1, which is composed bythe librations around they and z axes peaked at∼ 600cm−1 and around thex axis, peaked near 850 cm−1. Thelarge width of the librational band reveals the structural in-homogeneity of the H-bond network and the importance of

thermal fluctuations at ambient conditions. These molecularmotions can be directly or indirectly captured by a varietyof spectroscopic measurements.

0 0.2 0.4 0.6 0.8t / ps

-0.5

0

0.5

1

Cv,

Γ(t)

0 0.05 0.1 0.15 0.2t / ps

0 200 400 600 800 1000

ω / cm-1

0

0.5

1

ω2

Cv,

Γ(ω) /

Cm

ax

200 400 600 800 1000

ω / cm-1

0

1

2

3

vO v

H ___ Γx

- - - Γz...... Γy

O H

Figure 1. Normalized time correlation functions for the linear andangular velocities of water obtained from MD simulations usingthe SPC/E model and the corresponding frequency spectra. a)TCFs for the velocities of the oxygen and hydrogen atoms; b) TCFsfor angular velocities; c) Frequency spectra for the atom velocityTCFs; Frquency spectra for the angular velocity TCFs (the linewith symbols is the sum of the individual spectra).

3 Dielectric Response

Dielectric relaxation techniques are among the oldest andmost popular methods to extract information about the sys-tem’s dynamics over a wide range of frequency values. Thekeen interest in the dielectric behavior of polar liquids islargely due to the fact that these properties are essential tocharacterize the liquid as a reactional medium for chemi-cal processes involving ionic or polar species[19]. Dielec-tric properties such as dielectric constants, dielectric relax-ation times, frequency dependent far infrared (FIR) absorp-tion coefficients, and longitudinal dielectric relaxation timesare key ingredients to the description of a variety of physic-ochemical phenomena, specially solvation dynamics andcharge transfer reactions[20]. In very simple physical terms,the dielectric response relies on the absorption of radiationby matter that occurs when the frequency of the incident ra-diation matches the dynamical fluctuations of the sample’stotal dipole moment. Within a linear response framework,the frequency dependent complex dielectric permittivity isrelated to the Fourier transform of the system’s collectivedipole moment TCF:

c

ε(ω)− ε∞ =1

3 V kB T ε0

[〈|M(0)|2〉+ i ω

∫ ∞

0

dt 〈M(t) ·M(0)〉 eiωt

]. (1)


Such time correlation functions can be computed fromlengthy molecular trajectories generated from an MD simu-lation and then Fourier transformed to yieldε(ω). One of theearliest and most complete set of MD simulations aimed atthe dielectric response of water is reported by Neumann[21]using the TIP4P water model[22]. The real and imaginaryparts ofε(ω) as function of frequency up to2× 1014 Hz (∼1000 cm−1) are depicted in Fig.2 by the upper and lowercurves. Solid and dotted lines correspond, respectively, tosimulation and experimental results, obtained from differ-ent spectroscopic measurements[6, 7]. Starting from upperfrequencies, one notices inIm ε(ω) sharp absorption fea-tures due to the internal molecular vibrations, followed bya broader band around 1014 Hz which is due to the inter-molecular librational motions. Next to it, atω ∼ 3 × 1013

Hz (150-200 cm−1) there is another resonance which it notcaptured by the TIP4P simulations. At much lower frequen-cies, a broad absorption band appears in the microwave re-gion resulting from the rotational-diffusion reorientationalmotions of the water molecules with a typical dielectric re-laxation or Debye time around 10 ps. This dynamics is welldescribed by the simulations, although not apparent in theresults shown in Fig.1 because these TCFs wane long beforethe onset of slow molecular reorientational processes. Over-all, the simulations describe very well the dielectric spec-trum of water. The internal vibrations are easily reproducedusing a flexible model for water. The absorption at 150-200cm−1 was later shown to stem from hindered translationalvibrations of the molecule in the cage formed by its neigh-bors, just as portraied by the dynamics of the O atoms shownin Fig.1. Indeed, purely translational motions in a systemof nonpolarizable molecules such as TIP4P water have onlyan indirect influence on the fluctuations of the total dipoleM(t). When polarizability is taken into account, the trans-lational resonance is well reproduced[23].

Figure 2. Real and imaginary parts of the frequency dependent di-electric permittivity of water obtained from MD simulations on theTIP4P model (solid lines; Ref.[21]) and experimental data obtainedfor different regions of the spectrum (dotted lines; Refs.[6, 7])

3.1 Water in DMSO

Dimethylsulfoxide (DMSO) is a highly polar (µ ≈ 4.3D)aprotic solvent which mixes with water in all proportions atambient conditions. The DMSO molecule has an exposedsulfonyl oxygen which acts as a strong hydrogen bond ac-ceptor. For more than forty years, a keen interest has grownover this substance because of its many practical applica-tions in biomedical sciences, industry, and as a mediumfor chemical reactions[24] Upon mixing, water and DMSOexhibit interesting changes in thermodynamical, structural,dynamical, and H-bond network properties. In particular,these mixtures present very large deviations from ideal mix-ing behavior near the composition 33% DMSO, which hasbeen attributed to the formation of strong H-bond aggre-gates composed of one DMSO and two water molecules(1DMSO:2water). These changes and their molecular originhave been the subject of several MD simulation studies[25].Analyses of the structure and hydrogen (H)-bond distri-butions reveal different types of molecular associations,with the prevalence of 1DMSO:2water H-bond aggregatesof nearly tetrahedral ordering for water-rich mixtures and2DMSO:1water linkages for DMSO-rich solutions[26]. Thetranslational and reorientational dynamics of these mixturesinvestigated through MD simulations are in good agreementwith experimental NMR data[27], showing minima for theself-diffusion coefficients and slowest reorientational dy-namics for mixtures with composition near 33% DMSO.Simulation studies of the dielectric relaxation[28] over thewhole composition range yield results consistent with avail-able measurements[29] and unveils important microscopicdetails about the behavior of these mixtures.

One of the most interesting MD results on DMSO/watermixtures is the prediction of stable aggregates of compo-sition 2DMSO:1water in DMSO-rich mixtures[26]. Whilethe existence of 1DMSO:2water aggregates seems self-evident in view of the mixing behavior exhibited by sev-eral physcochemical properties, unambiguous experimentalevidence for the 2DMSO:1water aggregates found in thesimulations is still lacking. One of the most conspicuouscharacteristic of the 2DMSO:1water molecular aggregate isthat the central water molecule is flanked by two massiveDMSO molecules which strongly interact with it through H-bonding. This “bound” water molecule, being situated in aDMSO-rich microenvironment, is expected to present verydifferent short-time, librational dynamics than that foundin pure water. Indeed, our simulations[26, 28] of the far-infrared absorption coefficient for the pure liquids and formixtures of different compositions predicts an “splitting”of water’s librational band (600-800 cm−1) for DMSO-richmixtures, as shown in Fig. 3. TheF (ω) spectra are approx-imately given byω Im ε(ω) for each system and can be di-rectly obtained from experiemntal far-infrared spectroscopy.

Additional MD analysis permitted a clear identificationof the molecular origin for the splitting of water librationalband in the presence of DMSO. The calculated spectral char-acteristics of the TCFs for the angular velocity componentsfor pure water and a mixture with 80% DMSO is shown


in Fig.4 (a schematic drawing of the 2DMSO:1water ag-gregate is presented on top). The spectrum for pure waterconsists of the overlap of the individual spetra for each prin-cipal component, was mentioned before. In a DMSO-richenvironment the spectrum for the angular velocity decon-volutes into two submaxima due to the narrowing of eachcontribution. The peak in the spectrum forΓx shifts fromabout 850 in pure water to 750 cm−1 in the 80% DMSOmixture, indicating that the rapid small-amplitude rotationsof the water molecule about thex axis is less hindered in themixture. This has been rationalized in terms of the aggregatedrawn in Fig.4, in which the H-bonding donor character ofthe water molecule is similar to that in pure water, whereasits acceptor character is very distinct. With practically noH-bonding to its oxygen atom in these environments, thewater molecules experience very little restoring forces offthe plane of the sheet, thus rendering librations about thexaxis less hindered[28].

Figure 3. Simulated far-IR spectra for pure DMSO, pure water andtwo selected DMSO/water mixtures, indicated by the mole fractionof DMSO. The spectrum for pure water has been divided by 3 tofit the scale of the figure.

3.2 Supercritical water

Supercritical states of water provide environments with spe-cial properties where many reactive process with importanttechnological applications take place[30]. To give just oneexample, water under supercritical conditions (T > Tc =647K) is an extremely powerful, and environmentally be-nign, oxydizing agent with important applications in thetreatment of industrial toxic wastes. Two key aspects com-bine to make chemical reactivity under these conditions sopeculiar: The solvent high compressibility, which allows forlarge density variations with relatively minor changes in theapplied pressure, and the drastic reduction of bulk polarity,clearly manifested in the drop of the macroscopic dielec-tric constant fromε ≈ 80 at room temperature toε ≈ 6at near-critical conditions. From a microscopic perspective,the unique features of supercritical fluids as reaction media

are associated with density inhomogeneities present in thesesystems[31].

Figure 4. Frequency spectra for the normalized time correlationfunctions for the principal components of the water molecules’ an-gular velocity in pure water (thick lines) and in an aqueous mix-tures with 81% DMSO (thin lines). The drawing is a schematic ofthe 2DMSO:1water H-bonded aggregate predicted by MD.

Recently, microwave spectroscopy measurements havebeen reported for SCW at several different densities rang-ing from ρ = 1 down to 0.1 g/cm3, in an attempt to pro-vide valuable characterization of the dynamical nature ofsuch reaction media[32]. By fitting the measured frequency-dependent dielectric permittivity with a single Debye disper-sion relation, Okadaet al.[32] have found that the dielectricrelaxation timeτD presents a non-monotonic density depen-dence, with an unexpected branch forρ < 0.4 g/cm3, show-ing a rapid increase ofτD with decreasing density. This in-teresting feature could lead to distinctive dynamical solventeffects on molecular or ionic probes in solution. This resultsis surprising because one expects faster, not slower, dipolereorientation as the intermolecular interactions get weakerwith decreasing bulk density. In order to investigate themolecular origin of this intriguing effect, we carried out aseries of MD simulations for several supercritical thermo-dynamic states of water with densities ranging from 0.05 upto 1.0 g/cm3[33]. Not so much to our surprise, the dielec-tric relaxation time as function of density for temperaturesaboveTc (Fig.5) agrees very well with the experimental datafor ρ > 0.4 g/cm3, but fails to reproduce the rise inτD as the


density decreases below this value. The origin of such dis-crepancy is still not entirely clear, but our analysis indicatethat the behavior of the dielectric relaxation time is consis-tent with the theoretical free-rotor limit asρ → 0. The MDanalyses[33] also show that the dielectric response is highlynonexponential in the low density regime, which then indi-cates that the experimental estimates forτD obtained froma single Debye fit to the spectra may be highly uncertain.Interestingly, another simulation work, using a much moresofisticated, polarizable water model, was latter publishedcorroborating our results[34]. We believe that further inves-tigations in this area are surely needed.

0.0 0.2 0.4 0.6 0.8 1.0ρ/g cm-3

0.0

2.0

4.0

6.0

8.0

τ D/p

s

MD Exp.

315K

340K

450K

720K

Figure 5. MD and experimental Debye dielectric relaxation timesfor supercritical water as functions of density. When not indicated,the temperature is 650 K. The lines are drawn as guides to the eye.

4 Time resolved fluorescence

Considerable experimental and theoretical efforts have beendevoted to the study of molecular mechanisms of solvationdynamics, that is, the relaxation of the surrounding solventmolecules in response to sudden changes in the spectro-scopic solute probe’s charge distribution, which are usuallybrought about a photoinduced transfer of electronic chargesfrom one side of the probe molecule to the other[35, 36].The study of solvation dynamics at a molecular level com-prises an important step towards obtaining a deeper under-standing of the dynamical effects of the solvent environmenton electron and other charge transfer reactions in solution,and in broader sense of the effects of solvent dynamics onchemical reactions.

Time-dependent Stokes shift spectroscopy providesone means to experimentally access the dynamics ofsolvation, specially for macroscopically homogeneousenvironments[35, 36]. In these experiments, the data areusually reported in terms of normalized spectral response

functions describing the temporal evolution ofS(t) =[ν(t)−ν(∞)]/[ν(0)−ν(∞)], whereν(t) refers to the max-imum of the emission band at timet. In MD simulations,the photoexcitation is treated within the Frank-Condon ap-proximation, in which the solute’s ground and excited statesusually differ only by their charge distributions. The corre-sponding solvation response function is given by

S(t) =〈∆E(t)−∆E(∞)〉ne

〈∆E(0)−∆E(∞)〉ne

(2)

where∆E(t) = US1el (t)−US0

el (t) is the difference betweenthe S1 and the S0 Born-Oppenheimer potential energy sur-faces and〈...〉ne denotes an average taken over the nonequi-librium trajectories. This requires knowledge of the excitedand ground state charge distributions of the solute probe,which is usually obtained from quantum chemical electronicstructure calculations. The family of organic dyes known ascoumarins are among the most popular chromophores usedto investigate solvation dynamics in liquids. Coumarin 153(C153) is one of them.

4.1 Binary aqueous mixtures

Our studies on the solvation dynamics of aqueous systemshave focused on binary mixtures of water-methanol[37] andmore recently on water-DMSO mixtures. For the latter,we have performed studies using a simplified monoatomicmodel for the solute[38] in which we were able to iden-tify important contributions from water translational mo-tions to the solvation dynamics, manifested as a surprisingnegative branch on the individual co-solvent contributionsto the total solvation response. Our MD studies on solvationdynamics of water-DMSO systems have been extended to-wards a more realistic description of the organic dyes[39]using a more elaborate all-atom model for the coumarinC153 in which we sought direct comparison with very re-cent experimental upconversion fluorescence spectroscopymeasurements. Nonequilibirium simulation results for thesolvation responseS(t) of C153 in the neat liquids and var-ious water-DMSO mixtures are shown in Fig.6a. One cansee that the solvation dynamics of the aqueous systems ex-hibit an ultrafast initial relaxation within tens of femtosec-onds, which becomes less prominent as DMSO is addedto the system. The fast oscillations exhibited by theS(t)responses stem from the fast librational motions of watermolecules. The post-librational regime is characterized bya bi-exponential decay stemming from rotational-diffusionprocesses with some translational contributions. In all cases,the solvation dynamics is completed almost entirely on asubpicosecond time scale. The relaxation is most sluggishfor mixtures of composition near 25% DMSO, in accor-dance with previous simulations and experimental resultson diffusional processes of these mixtures. Our MD resultsshow excellent agreement with time resolved experimentaldata (Fig.6b)[40] after taking into account the finite resolu-tion of the experimental setup through a convolution of theMD data with an instrument response function.


0 0.2 0.4 0.6t (ps)

0.0

0.2

0.4

0.6

0.8

1.0

S(t)

waterx

D=0.25

xD

=0.50

xD

=0.75

DMSO

0 2 4 6

t(ps)

0

1

2

3

4

5

6

S(t

)

expMD

1.00

0.75

0.50

0.32

0.25

Figure 6. Nonequilibrium solvation responses for pure water andDMSO and selected DMSO/water mixtures obtained from MDsimulations using an all-atom model for the coumarin C153.

4.2 Hydrated electrons

The hydrated electron (an excess electron trapped into thesolvent) is an excellent probe for time-dependent spectro-scopies because of its large optical cross-section and the suf-ficiently long lifetime of the first excited state[41]. From thetheoretical viewpoint, the solvated electron is also the pro-totype system for mixed quantum-classical (MQC) simula-tions and has been extensively used in the development ofnew computational methodologies and the exploration of avariety of new physical phenomena in condensed media[42].In such MQC simulations the dynamics of the quantum par-ticle (the electron) is fully described within the bath of clas-sical solvent molecules. Previous simulation studies of thenonadiabatic relaxation from excited states[43] and the dy-namics of solvent reorganization in response to the photoex-citation of a self-trapped electron in aqueous solution[44]have revealed that the dynamical behavior of this systemis extremely rich. In summary, the solvation dynamics re-sponse resembles that of classical solutes in polar liquids,with an initial Gaussian decay characterized by a∼ 17 fsdecay time, followed by a slower (250 fs) exponential decaycomprising roughly 60% of the relaxation. However, unlikemost classical perturbations, the solvation mechanisms in-volve considerable solvent translational motions in order toaccommodate the changes in shape and size of the electronicwavefunction upon photoexcitation (from ans−like ground

state to ap−like first excited state) or after a nonadiabatictransition (fromp− to s−like states). The relative impor-tance of fast solvent librations in comparison with transla-tional motions to the different stages of solvation processwas not entirely clear for the hydrated electron.

0 100 200 300 400t (fs)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Cd (

t)

0.6

0.7

0.8

0.9

1

Cd (

t)

(a)

(b)

Figure 7. Comparison between simulation and experimental sol-vation responses for C153 in DMSO/water mixtures (thick lines)after convolution of the MD response with a Gaussian function rep-resenting the instrument time resolution. The Gaussian is centeredat 200 fs for pure DMSO and thexD = 0.75 solution, and at 140fs for the other mixtures.

Very important and extensive theoretical work on sol-vated electrons have been carried by the Rossky group. Fur-ther understanding of the dynamical behavior of hydratedelectrons has been reached by applying the instantaneousnormal mode (INM) theoretical framework of liquids toMQC simulations[45]. From the very extensive analysis ofthat work, we will discuss here only the relative contribu-tions from the different types of solvent motions to the elec-tron solvation response that we extracted from the INM for-malism. Consistently with a variety of spectroscopic mea-surements on liquid water, we have separated the motionswithin INM according the frequency ranges: Diffusive: 0 –400 cm−1; Librational: 400 – 1200 cm−1; Bending: 1500– 2200 cm−1; and Stretching: 2200 – 4600 cm−1. Fig. 7shows the normalized partial solvation responses from thefour frequency ranges for the upward (panel a) and down-ward (panel b) electronic transitions. The partial responsesexhibit similar features for both cases. The internal bendingand stretching motions are seen to contribute to the solva-tion responses only at very early times, typically below 5-10 fs, which may possibly impact quantum decoherence ofthe electronic states. The fast librational motions dominatemost of the response in the first 25 fs and is also the causeof the recurrence in the total response functions at∼ 40 fs.Diffusive motions also come in at early stages of the solva-tion process, being the predominant relaxation channel fromabout 50 fs and on. This result indicates the importance oftranslational dynamics to the solvation response in these sys-tems and shows that the combination of librational and dif-fusive motions comes in at an early stages of the solvation


response of the hydrated electron. Moreover, the character-istics of the diffusive contributions are distinct from thoseof the librational and single-molecule internal modes. In thephenomenological Brownian oscillator picture, the formerbehaves like an overdamped oscillator, whereas the behav-ior of the librations and intramolecular vibrations is typi-cally underdamped. From the viewpoint of the INM theory,these features stem from the different degrees of localizationof the diffusive, librational, and internal motions. Furthercomparison of panels (a) and (b) of Fig.7 suggests that bothlibrational and diffusive contributions are slightly larger forthe downward than for the upward transition. This differ-ence is clearly associated with the spatial shrinkage of theelectron wavefunction for the downward transition whichcreates a void readily occupied by the neighboring solventmolecules, starting with the rapid dragging in of the lighthydrogen atoms.

4.3 Electrons in supercritical water

Another interesting problem where mixed quantum-classical simulations contributed with new physical insightsis that of the quantum states of excess electrons solvated insupercritical fluids. In normal dense fluids, the ground andfirst few excited state wavefuctions for the solvated elec-tron are spatially localized in a roughly spherical region notmuch larger than a halogen anion due to the interactions withthe surrounding solvent molecules. In a hypothetical situa-tion in which the number density of the solvent environmentis gradually reduced down to nearly zero, one would expectthe excess electron wavefunction to change from a spatiallylocalized to a delocalized, quasifree state over the entire vol-ume nearρ = 0, resembling the text-book problem of a par-ticle in a box. With supercritical fluids, this situation can inprinciple be materialized since the density can be drasticallyvaried by small variations of the external pressure[31].

For many years, a series of pulse radiolysis experimentshas provided evidence that electronic states can be supportedin aqueous supercritical environments[46, 47, 48] and thatthe spectral characteristics of solvated electrons can be usedto investigate the structure of the local inhomogeneities insupercritical systems[49]. It is generally believed that agradual transition from localized states, typical of dense po-lar fluids, to quasifree electronic states under supercriticalconditions leads to the observed red shifts in the optical ab-sorption spectra and to significant changes in the dynamicalbehavior of the electron, most notably a dramatic increasein its drift mobility[50]. However, experimental[46] absorp-tion spectra of nearly supercritical water atT = 623 K ex-hibit a weak density dependence of the spectral shift over awide interval ranging from 1 g cm−3 down to 0.05 g cm−3,thus suggesting that the electron localization in aqueous su-percritical environments persists at density as low as 0.05 gcm−3.

Laria and Skaf[51] recently addressed this problem bysimulating an excess quantum electron in a bath of classi-cal water using Feynman Path Integral MD techniques. Thisformalism explores the well-known isomorphism betweenthe statistical mechanics of the quantum electron path and

that of a classical cyclic polymer containing pseudoparticles(“beads”) with harmonic nearest neighbor interactions. Themost direct route to analyze the extent of the electronic lo-calization is by examining the behavior of the mean squarecorrelation function for the solvated electron-polymerR2(t)defined by:

R2(t− t′) = 〈|r(t)− r(t′)|2〉 , 0 ≤ t− t′ ≤ β~ ; (3)

wherer(t) represents the electron position at imaginary timet andβ−1 is Boltzmann constant times the temperature. Atlow densities (ρw < 0.1 g cm−3), the correlation func-tions (Fig. 8, left panel) look similar to those correspond-ing to Gaussian free polymers: Interparticle distances alongthe electron polymer are characterized by a wide varietyof lengthscales, up to roughly half the de Broglie thermalwavelength,λdB(T = 645 K) ≈ 12A. As we move towardsthe density regime of typical dense fluids, there is a qualita-tive change in the temporal behavior of the curves. After ashort transient lasting≈ 0.1β~, the curves level off at practi-cally plateau values. This time independence has been inter-preted as a signature of statistical dominance of the groundstate on the behavior of the electron. Expressed in terms ofthe spectrum of instantaneous electron eigenvalues, this sit-uation corresponds to large energy gaps (À kBT ) betweenthe ground and the manifold of excited states. More di-rect evidence of this transition is acquired by inspecting thedensity dependence of the correlation length for the elec-tron polymerR = R(β~/2), shown in the right panel ofFig.8. The sudden drop to practically half of the ideal, non-interacting,ρw = 0 value within a narrow density intervaland an abrupt change in the slope of the curve, reveal the on-set of the electronic localization atρw ≈ 0.15 g cm−3. Fordensities well below the localization threshold, one can seethe electron wavefunction tunneling across the surroundingwater molecules.

0.0 0.1 0.2 0.3 0.4 0.5t(βh)

0.0

0.2

0.4

0.6

0.8

1.0

R/(

0.75

1/2 λ dB

)

0

2

4

6

8

10

R (Å

)

0.0 0.2 0.4 0.6 0.8 1.0ρw(g cm

−3)

Figure 8. Left: Root mean square correlation function for the ex-cess electron in supercritical water along theT = 645 K isotherm.Lines from top to bottom correspond toρw =0.0 (free electron),0.05, 0.1, 0.3, 0.5, 0.7, and 1.0 g cm−3, respectively. Right: Cor-relation length for the electron polymer vs. density. The arrowindicates the room temperature result.


The optical absorption spectra for supercritical states ofwater were also computed from our simulations and they re-produce the experimental values reasonably well, althoughthe density dependence of the spectral red shift in the range0.1 g cm−3 ≤ ρw ≤ 0.5 g cm−3 is somewhat more pro-nounced than that experimentally measured. Interestingly,there are apparently no noticeable changes in the density de-pendence of the spectral band maximum as the localizationtransition is crossed.

5 Ultrafast optical Kerr effect

The optical Kerr effect (OKE) ultrafast laser spectroscopy ispart of a large family of multiple-wave mixing processes thatexploits nonlinear optical responses of the material to ex-tract information on its ultrarapid intra- and intermoleculardymamics directly in time domain[14]. OKE spectroscopyhas been successfully applied to extract dynamical informa-tion of a large variety of pure liquis, mixtures, and confinedfluids[52]. In liquid water, the nonlinear optical signal isdominated by the electronic polarizability response, as themotion of the nuclei provides less than 5% of the total re-sponse. This increases the degree of uncertainty in obtain-ing the dynamics of water and here is where MD simulationscome in.

The optically heterodyne-detected OKE signal in thetime domain reflects the third order electric susceptibilityof the sample and provides valuable information about theintermolecular dynamics through the nuclear response func-tion,Rnuc(t). This quantity is experimentally obtained fromthe raw OKE transients after removal of the instantaneouselectronic response and deconvolution from the instrumentfunction[53].Rnuc(t) can also be fairly easily obtained froma sufficiently long set of MD trajectories by simply comput-ing the time derivative of the anisotropy collective polariz-ability TCF through:

Rnuc(t) = −Θ(t)kBT

∂Ψ(t)∂t

, (4)

where Θ(t) is the Heaviside step function andΨ(t) ∝〈Πxz(t) Πxz(0)〉 is the TCF of the polarizabilityanisotropy, with

Π =∑

i

αi = ΠM + ΠI , (5)

where the total polarizability has been separated into intrin-sic (molecular),ΠM , and induced,ΠI contributions. Theintrinsic part is the sum of unperturbed, gas phase molecularpolarizabilities properly rotated into the lab frame of ref-erence, while the induced counterpart is computed throughsome induction or modulation scheme such as the dipole-induced-dipole mechanism.

We have studied the OKE response for pure water andalso in water-DMSO mixtures using molecular polarizabil-ity and hyperpolarizabiliy tensors obtained from electronicstructure calculations at the MP2/6-311++G(d,p) level inour MD simulation analysis[54]. The results forRnuc(t)

of liquid water are shown in Fig.9, along with the perma-nent or molecular polarizability autocorrelation, induced po-larizability contributions and the cross-correlation betweenpermanent and induced anisotropies. The simulated OKEnuclear response exhibits a very rapid rise within the ini-tial stages, showing local maxima near 15, 50, and 180 fs,followed by a diffusive tail which has been fitted by a bi-exponential with time constants∼ 0.2 and 2.0 ps. The shorttime features are in good agreement with previous simula-tions as well as with experimental results reported by Cast-ner et al.[55], which shows peaks at∼20, 57, and 197 fs.The agreement with experiments is less satisfactory for thediffusive components. Figure 9 also shows that the first peakis almost entirely given by fast molecular reorientational thatclearly associated to librational motions, while the subse-quent maxima stem from a combination of permanent andinduced contributions. The maximum near 180 fs seemsto have important contributions from translational dynam-ics as indicated by the amplitude of the induced term aroundthat time window. The hindered translational motions of theO atoms comprise the underlying molecular mechanism forthis feature.

0 0.1 0.2 0.3 0.4

t / ps

0

4

8

12

16R

nuc (t

) [

arb.

un.]

total

induc.

cross

perm.

Figure 9. The OKE nuclear response function for water obtainedfrom MD simulations. The total response and the separate contri-butions are as indicated.

These response functions can be appropriately Fouriertransformed to represent either the frequency spectrum ofthe Kerr signal or the Bose-Einstein corrected depolarizedRaman spectrum. Although we do not show these spectrahere, it is important to mention that the simulated OKE spec-trum for water exhibits a rotational-diffusion peak centeredaround 3 cm−1, a collision-induced (hindered translations)band near 200 cm−1, and a broad librational band at 450cm−1. These results are in good agreement with experimen-tal frequency spectra obtained from Kerr effect and relatedspectroscopies. There are, however, noticiable discrepan-cies in the vicinity of 60 cm−1, indicating shortcomes in ourmodeling of the polarizability fluctuations of water.


6 Vibrational Dephasing

Vibrational dephasing refers to the lost of coherence by acollection of oscillators coupled to a solvent bath[56]. Imag-ine an oscillator whose vibrational motion is being perturbedby the fluctuating interactions with the surrounding solvent.The phase of the oscillations will soon go random due tothe fluctuations in the intermolecular potential. In this phe-nomenon, both the timescale and magnitude of the forcefluctuations are important[57]. Valuable information aboutthe solvent dynamics can be extracted from a vibrational de-phasing analysis of Raman lineshapes if a sensitive Ramanprobe is used. In recent years, vibrational dephasing havealso been investigated directly in the time domain using ul-trafast laser spectroscopies such as Raman echo or Ramanfree-induction decay[13].

The monocyclic dianions, CnO2−n (3 ≤ n ≤ 6), known

as oxocarbon dianions comprise a family of excellent Ra-man probes[58]. The squarate (n = 4) and croconate(n = 5) ions exhibit unusually high Raman intensities forboth totally symmetric and non-totally symmetric modes,with relatively well-separated bands. Such a distinctiveproperty has been used to examine the Raman lineshapesof modes of different symmetries in aqueous solutions, thusproviding an experimental route the reorientational dynam-ics about the in-plane and out-of-plane symmetry axes of theoxocarbons[58]. Detailed analyses based on the isotropicand anisotropic components of the totally symmetric ringbreathing mode, along with the anisotropic parts of the non-totally symmetric C-C stretching and ring bending modes,indicate that reorientation of the oxocarbon anions is veryhindered in water, with comparable decay rates for spinningand tumbling of the main symmetry axis. Vibrational de-phasing analysis predicted small relaxation times (∼0.1 ps)of the vibrational frequency fluctuations. This fast modu-lation together with the observed slow rotational-diffusiondynamics suggests a picture where the ions undergo rapidlibrational motions inside solvent cages, which are continu-ally formed and disrupted on a timescale that should exceedseveral times the characteristic librational period.

Indeed, our recent MD simulation studies of the squaratein water show the existence of a well-defined hydrationshell, composed of an average of 12 water molecules H-bonded to the carbonyl oxygens (three water moleculesper oxygen atom) which is preserved for more than 20-30ps[59, 60]. The dynamics is isotropic and the anion libratesat 70 and 250 cm−1[60]. In a separate MD study, we havealso investigated more closely the features of the vibrationaldephasing of this species in water. Within the classical the-ory of vibrational dephasing, the instanteneous shift in thevibration frequency of modeα is related to solvent resultantforces along the coordinates of the normal mode of interestduring the simulations, the anharmonicity constants,φαβγ ,and the atomic displacements of each mode,Lα

m, which areobtained from a quantum chemical vibrational analysis ofthe isolated molecule[56]:

δωα(t) =modes∑

β

φααβ

soluteatoms∑m

LβmFm(t) (6)

The quantity of interest is the frequency shift dynamicalfluctuations:

χα(t) = 〈∆ωα(t)∆ωα(0)〉 ; ∆ωα(t) = δωα(t)− 〈δωα〉(7)

from which one can compute the dephasing time1/Tα2 =∫∞

0χα(t)dt for direct comparison with experimental mea-

surements.Out of all normal modes of the squarate dianion, the

C=O stretching (ν1) and ring breathing (ν2) modes are par-ticularly interesting because their use in the experimentalanalysis. The ring breathing dephasing time obtained fromthe simulations (0.08 ps) is in close agreement with the ex-perimental estimates (0.06 ps). The frequency shift corre-lation function separated in terms of the purely Coulom-bic, χC(t), and short-ranged dispersive (Lennard-Jones)forces,χLJ (t), for these two vibrational modes are shown inFig.10. The results show that the electrostatic forces contri-butions to the dephasing exhibit fast dynamics at early times,clearly associated to the rapid motions of water hydrogenatoms, that is, solvent librations, but also present a slowercomponent at longer times due to long-range nature of theCoulombic interactions. The dispersive contributions, onthe other hand, fluctuates with larger timescales because itenvolves motions of the oxygen atoms (the hydrogens havevanishing dispersive interactions), but show no long-timetail sinceχLJ (t) is essentially determined by the short-rangestructure of the liquid. Fig. 10 also shows the dephasing re-sponses for each mode with (thin lines) and without (thicklines) the anharmonic couplings between modes (cf. Eq.6).One sees that mode coupling affects essentially the LJ partof the dephasing correlation function for the C=O stretching,leaving the other correlations practically unaltered.

7 Water near interfaces

The heterogeneous nature of interfacial liquid/liquid sys-tems have long been a subject of keen interest to scientistsand motivated widespread studies about microphysical be-havior at interfaces. At molecular scales, the system’s bro-ken symmetry imposes a nonconventional ambient in theimmediate vicinity of the interface, resulting in a molecularbehavior that can be much different from that found in thebulk liquid phase. Liquid interfaces also play an importantrole in biological systems, such as membranes and proteinsouter surfaces, and in colloid sciences, which very often in-volve systems of great practical and technological impor-tance. In recent years, new approaches based on nonlinearspectroscopic methods have provided important insights anddetailed information about the structural and dynamical be-havior of molecules at interfaces[61, 62]. While a great dealof our current knowledge on interfacial systems has been ob-tained from measurements of thermodynamic macroscopicproperties, nonlinear spectroscopic techniques such as Sec-ond Harmonic Generation (SHG) and Vibrational Sum Fre-quency (VSF), have made it possible to investigate the be-havior of molecules located in the vicinity of the interfacewithout the interfering signal from molecules situated in thebulk[61, 62].


0.0

0.2

0.4

0.6

0.8

1.0

χ C(t

)ν2ν1

ν2acopl

ν1acopl

0 0.2 0.4 0.6 0.8

t(ps)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

χ LJ(t

)

Figure 10. Dephasing responses obtained for the C=O stretching(ν1 and ring breathing (ν2) modes of the squarate anion in water.The upper and lower panel depicts the Coulombic and dispersivecontributions, respectively.

Of particular interest, the water/carbon tetrachloride(H2O/CCl4) interface emerges as an important prototype forhydrophobic interacting systems that grossly mimic biolog-ical membranes, and as a natural support media for surfac-tant systems in molecular simulation studies. In addition,the CCl4 molecules are quite insensitive to infrared radia-tion absorption, eliminating possible interferences in non-linear spectroscopy of interfacial water molecules. Very re-cently, we have performed extensive MD simulations for theH2O/CCl4 liquid/liquid interface aiming at elucidating thegeneral structural and dynamical features of this interface ata microscopic level[63]. We present next MD results regard-ing the orientation of water molecules near the interface andhow it influences the dynamics of interfacial water. The sim-ulations were performed using models that include internalvibrations.

The average orientation of the water molecules with re-spect to the plane of the interface is an important structuralfeature that can be determined from the normalized proba-bility distribution for the angle between the water dipole andthe Z axis (normal to the interface), and also for the angle be-tween the Z axis and the vector joining the hydrogen atomsof a given molecule. For clarity, we denoteµz andHHz theZ components of the unitary dipole and HH vectors, respec-tively. The results are depicted in Fig.11a and 11b for bulk(dashed lines) and interfacial (solid lines) water molecules.For comparison, Fig.11a also shows the distribution of thedipoles’ Z components for an intermediate region between

0

3

6

9

12

0 30 60 90 120 150 180 θ ( degrees )

0

3

6

9

12

103 x

P(θ)

0 4 8 12r (Å)

0

0.01

0.02

0.03L

ocal

den

sity

(A

.U)

µz

HHz

bulk

interface

HO

a)

b)

c)

Figure 11. Probability distributions for the angle between the Zaxis (normal to interface) and the unit dipole (panel a) and HHvectors (panel b) for bulk and interfacial regions obtained from MDsimulations of a water/CCl4 liquid/liquid interface.

bulk and interface (dotted line). For an isotropic environ-ment such as bulk liquid, the orientation of any molecularvector follows an uniform distribution, which in polar coor-dinates is simply given byP iso(θ) = 1/2 sin(θ). Indeed, thebulk distributions shown in Fig.11 are sinusoidal. As one ap-proaches the interface, there is a relative enhancement in thepopulation of water dipoles oriented parallel to the interfacewith the concomitant decrease in the probability of finding awater molecule with the main symmetry axis pointing acrossthe interface (Fig.11a). A similar behavior is observed forthe HH vectors (Fig.11b). However, in this case one no-tices a slight asymmetry in the distribution which impliesthat near the interface the HH vectors are, on the average,slightly twisted at angle from the interface plane. Similarconclusions have been reported in previous MD simulations


of this interface, although in less detailed molecular terms.Further support to this observation is provided by the localdensity of hydrogen and oxygen atoms as measured from thecenter of masses of CCl4 molecules located at the interface.Fig. 11c shows the local density for the H (solid line) andO (dashed line) atoms in arbitrary units. The local densityof H atoms is divided by two, such that at larger distancesit coincides with the local density of O atoms. Fig. 11cclearly shows that in going from the organic to the aqueousphase one would encounter a water hydrogen first. Analysisof the H-bond distribution shows that, near the interface, theaverage number of H-bonds per water molecule is only 2.7,indicating the presence of “free” OH bonds.

0 1 2 3 4

0

0.5

1

ω2

CvH

(ω)

3.2 3.4 3.6 3.8 4

ω / 103

x cm-1

0

0.5

1

ω2

CvH

(ω)

bulk

interface

Figure 12. Frequency spectra for the water hydrogen atoms veloc-ity time correlation for molecules in the bulk phase (upper panel)obtained from MD simulations. The lower band (< 1000 cm−1)is due to intermolecular librations and the two upper bands reflectthe bond bending and stretching modes. The lower panel shows thespectrum in the region of stretching modes for water near the CCl4

interface.

The dynamics of the water molecules in the vicinity ofthe CCl4 interface can be investigated in several differentways. One of the simplest and most elucidating form ofunveiling this dynamics is through the frequency spectrumof the hydrogen velocity TCF,CvH(t). Fig. 12 shows theCvH(ω) spectra of the hydrogen dynamics for bulk watermolecules. The intermolecular, librational band discussedbefore that appears below 1000 cm−1 is clearly seen for bothbulk and interface water. The sharp peaks near 1500 and3600 cm−1 stand for the bond bending and stretching inter-nal modes (symmetric and antisymmetric altogether). The

lower panel shows the spectrum in the region of the stretch-ing modes for water near the interface with CCl4. The spec-trum is remarkably similar to that obtained experimentallythrough VSF spectroscopy of this interface[61], thus rein-forcing the view that near these interfaces there should exist“free” OH bonds. Further research in this direction is cur-rently being conducted.

8 Ligand-protein dissociation

Water has also a fundamental role on the structure and dy-namics of biomolecules, particularly proteins. From thepoint of view of molecular dynamics simulations, this intro-duces significant challenges, since the complete solvationof a large biomolecule requires tens of thousands of watermolecules, increasing by orders of magnitude the computa-tional demand. Thus, it is common to neglect the effect ofwater molecules, even without rigorous studies on the roleof water in the simulations being performed.

One of the main fields where molecular dynamics simu-lations is able to provide valuable insights is the associationand dissociation pathways of ligands into or from their re-ceptors. Among these receptors a very important class isthe Nuclear Hormone Receptor Superfamily, which controlsthe activity of the most important hormones in vertebrates,such as the Retinoic Acid (Vitamin A), Estrogen and Thy-roid hormones, for example. The pathways of dissociationof the Retinoic Acid from its receptor RAR-γ were accessedthrough molecular dynamics simulations by Karplus andco-workers by a technique known as Enhanced SamplingMolecular Dynamics (ESMD) which is designed, basically,to reduce the potential barriers for ligand escape increasingthe dissociation rates [64]. This is achieved by simulating acollection of hormone replicas in the presence of a uniqueprotein in such a way that the replicas do not interact witheach other while the interaction with the protein is scaled bythe number of hormone replicas being used in the simula-tion. This permits the simulation of the dissociation path-ways in time scales accessible for MD simulations.

The simulations of Karplus and co-workers where per-formed without any water molecule due to the computa-tional cost of simulating the solvent. This was consistentwith the use of a technique where the potential parametersof interactions are approximated with the goal of increas-ing dissociation rates. They observed a mechanism that wasalready suggested in the literature [65] known as “mousetrap”, which is represented in Fig.13 and consists basicallyon the movement of the Helix 12 apart from the body ofthe protein, forming a cavity through which the hormonesscape. They observed this pathway in less than 100 ps, as isshown in Fig.13.

While there would be no great improvement on thesignificance of the results by the inclusion of the solventsince potentials were already approximated, it is not knownwhether the water molecules that actually belong to the crys-tallographic structure would be of any relevance to the dis-sociation pathway. This problem is particularly importantsince these water molecules belong to the protein in


Figure 13. Dissociation pathway of the retinoic acid from its receptor resembling the “mouse trap” mechanism obtained from ESMDsimulations in the absence of solvent molecules.

Figure 14. Detail of the dissociation pathway of the retinoic acid from its receptor showing stabilization of the protein structure through aH-bond network promoted by the presence of structural water molecules.

the sense that their residence time in the corrsponding po-sitions relative to the protein structure is very long com-pared water diffusion in bulk solvent [66]. We then per-formed ESMD simulations with the same protein, hormoneand techniques used by Karplus and co-workers to accessthe role of structural water molecules in the dissociationpathways proposed[67]. We performed four independentsimulations with 20 and 50 retinoic acid replicas, with andwithout the presence of crystallographic water molecules,for 200 ps each. The first simulation reproduced part of theresults presented in [64], revealing, indeed, the “mouse trap”mechanism in the same time scale as shown in Fig.13.

However, the simulation with 20 hormone replicas in thepresence of structural water molecules did not lead any hor-mone dissociation within 200 ps, which is more than twicethe time needed to dissociate in the absence of water. Thedetailed observation of the dynamics of the water moleculesin the region where the Helix 12 should loose its interactionsto the protein leading to dissociation in the 20 copies sim-ulation unveils important information about the interactionof water with key aminoacids. As shown in Fig.14, whilethe Serine in the bottom of the Figure belongs to the proteinbody, the Proline and Leucine at the top belong to the Helix12. Clearly, the water molecules form bridges of three orfour hydrogen bonded molecules between these aminoacids

throughout the course of the simulation. This restrains themovement of the Helix 12 and, thus, hinders hormone es-caping from the receptor’s cavity.

This result has shown that while the structural watermolecules did not promote a different pathway for disso-ciation, they significantly decrease the dissociation rate bystabilizing the protein structure. This is a novel and inter-esting example of the very important role that water playsto biomolecular structure and dynamics, and that it has anactive role on the functionality of protein structures.

9 Concluding Remarks

We have presented a review on the dynamical properties ofseveral aqueous systems focused largely on computer simu-lation work performed in our lab at the State University ofCampinas. With this mosaic, hope to have given the reader,specially the nonexpert in this field, a glimpse at the fasci-nating dynamical behavior of water.

Acknowledgements

The authors gratefully acknowledge FAPESP and CNPqfor supporting most of the work done in our lab. MSSwould like to thank Ivana A. Borin for the initial work onwater/DMSO mixtures. It is a pleasure to thank Professors


Daniel Laria, Mauro Ribeiro, Branka Ladanyi, Peter Rossky,and Igor Polikarpov for their wonderful collaboration.

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